Performance Analysis of Triangular Quadrature Amplitude Modulation in AWGN Channel

Recently, the triangular quadrature amplitude modulation (TQAM) whose signal points are regularly distributed at the vertexes of contiguous equilateral triangles was proposed. In this paper, we derive the general formula calculating the average energy per symbol of the TQAM and find out that the asymptotic power gain of the TQAM over the well-known square quadrature amplitude modulation (SQAM) is 0.5799 dB. We also analyze the symbol error rate (SER) and the bit error rate (BER) of the TQAM and compare them with the error performances obtained through computer simulation. Analytical and simulation results coincide at a wide range of signal to noise power ratio (SNR). The power gain increases gradually and approaches the asymptotic value as modulation order increases and target error rate decreases.

I. Introduction

In modern digital communication systems, high-order modulation is one of the useful physical layer techniques enabling high-speed data transmission and a large amount of literature exists on the issue of selecting an efficient signal set [1]–[6]. Especially, the square quadrature amplitude modulation (henceforth SQAM) proposed by Campopiano and Glazer in [3] is being widely used in numerous commercial communication systems. In the SQAM constellation, signal points are regularly placed at the vertexes of square lattice. Although the SQAM is not optimum in the sense of power efficiency, the quite good performance with simple detection makes it popular.